Let I $=($M$,$ W$)$ be an instance of the stable matching problem. Suppose that the preference lists

of all m in M are identical, so without loss of generality, mi has the preference list $[$w$1,$ w$2,...,$ wn$].$

Prove that there is a unique solution to this instance. Describe what the solution looks like, and why

it is the only stable solution. $($Note: showing that the solution is the one found by the Gale$-$Shapely

algorithm is not sufficient, as there could be other solutions.$)$